A01=Grzegorz Swiatek
A01=Jacek Graczyk
Affine transformation
Algebraic function
Analytic continuation
Analytic function
Author_Grzegorz Swiatek
Author_Jacek Graczyk
Automorphism
Big O notation
Bounded set (topological vector space)
C0
Calculation
Canonical map
Category=PBK
Change of variables
Chebyshev polynomials
Combinatorics
Commutative property
Complex number
Complex plane
Complex quadratic polynomial
Conjugacy class
Conjugate points
Connected component (graph theory)
Critical point (mathematics)
Diffeomorphism
Disjoint union
Disk (mathematics)
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equicontinuity
Existential quantification
Functional equation
Fundamental domain
Hausdorff distance
Holomorphic function
Homeomorphism
Homotopy
Hyperbolic function
Imaginary number
Implicit function theorem
Intermediate value theorem
Interval (mathematics)
Irreducible polynomial
Iteration
Jordan curve theorem
Julia set
Limit of a sequence
Linear map
Local diffeomorphism
Mathematical induction
Maxima and minima
Meromorphic function
Moduli (physics)
Monomial
Monotonic function
Open set
Periodic function
Point at infinity
Polynomial
Projection (mathematics)
Quadratic
Quadratic function
Quasiconformal mapping
Renormalization
Riemann sphere
Riemann surface
Schwarzian derivative
Subsequence
Theorem
Topological conjugacy
Topology
Union (set theory)
Unit circle
Unit disk
Upper half-plane
Product details
- ISBN 9780691002583
- Weight: 227g
- Dimensions: 197 x 254mm
- Publication Date: 25 Oct 1998
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics. In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students.
Jacek Graczyk is Assistant Professor of Mathematics at Michigan State University. Grzegorz Swiatek is Associate Professor of Mathematics at Pennsylvania State University.
